Greenʼs function for first-order multipoint boundary value problems and applications to the existence of solutions with constant sign

We consider a first-order linear differential equation subject to boundary value conditions which take into account the values of the function at multiple points in the interval of interest. For this problem, we calculate the Greenʼs function which allows to express in integral form the exact expression of the unique solution to the multipoint boundary value problem under the appropriate conditions. From this study, some results are derived concerning the existence of solutions with a constant sign (that is, some comparison results for first-order multipoint boundary value problems).